Response analysis of the nonlinear vibration energy harvester with an uncertain parameter

In this paper, the Chebyshev polynomial approximation is firstly utilized to analyze the dynamical characteristics of the nonlinear vibration energy harvester with an uncertain parameter. First, the stochastic energy harvester is transformed into a high-dimensional equivalent deterministic system by the Chebyshev polynomial approximation. And the ensemble mean response of the stochastic energy harvester is introduced to discuss the stochastic response. Then, the effectiveness of the approximation method is verified by numerical results. Furthermore, the bifurcation property of the displacement and voltage is analyzed, which is also consistent with the results derived by the top Lyapunov exponent. It is found that random factor can induce the appearance of multi-periodic phenomena and lead to appear the behavior of the periodic bifurcation. The strong random factor induces the fluctuation of the output voltage. In addition, the existence of the random factor greatly influences the property of the sub-harmonics and super-harmonics of the spectrum. Overall, the response mechanism of the nonlinear vibration energy harvester with an uncertain parameter is revealed.